THERE is something weird, almost uncanny, in the noiseless rush of the 'cyclist, as he comes into view, passes by, and disappears. Pedestrians and carriages are left behind. He yields only to the locomotive and to birds. The apparent ease and security of his movement excite our wonder. We have seen rope-walkers, and most of us have tried to walk on the top rail of a fence, and have a vivid recollection of the incessant tossing of arms and legs to keep our balance, and the assistance we got from a long stick or a stone held in our hands. But the 'cyclist gets no help. His legs move only in the tread of the wheel, and his hands rest quietly on the ends of the cross-bar of his machine. The rope-walker keeps every muscle tense, and every limb in motion or ready to move. No wonder, when a tourist on his bicycle spins for the first time through a village here, or among the nomads of Asia, he is followed by a gaping crowd, till his machine carries him out of their sight.

We involuntarily ask, How is it possible for one supported on so narrow a base to keep his seat so securely and, seemingly, so without effort?

For an answer to this question I have searched somewhat widely, and, while I have found articles enough on or about the bicycle, and what has been done by its riders, I have found none that offered a reasonable theory for its explanation. This is my apology for presenting the present paper. In it I shall state the theories which have been offered, the reasons why they are unsatisfactory, and then give what appears to me the true rationale of the machine.

The only paper I found that claimed to explain the bicycle was one by Mr. C. Vernon Boys, entitled The Bicycle and its Theory. It was delivered before a meeting of mechanical engineers, and is reported at great length in Nature, vol. xxix, page 478. Here, thought I, is something valuable and convincing. But, on examination, I found that, out of several pages of closely printed matter, the Theory occupied possibly a dozen lines. All the rest was about the bicycle and what had been done on it, but not another word about its theory. We are told that Mr. Boys exhibited a top in action, and requested his audience to notice its remarkable stability. Then he said that the stability of the bicycle was due to the same principle, but made no attempt to show any connection between them. The top revolves on its axis, and it stays up as you see; the wheel of the bicycle revolves on its axis, and therefore it stays up, was his theory and demonstration, and the whole of it, and, so far as one can judge from the report, he was satisfied, however it may have been with his audience.

Of all machines, none seem to be so little understood as the top and its near relation, the gyroscope. Hence the best that can be said is, that the lecturer availed himself of the tendency found in most minds to "explain" an unfamiliar phenomenon by referring it to some other more familiar one, longer known, but equally incomprehensible — as if, as in grammar, two negatives make an affirmative, so, in physics, two unknowns make a known.

Without going into the theory of the top, or of the gyroscope, it is easy to show experimentally that their stability and that of the bicycle must be due to different principles. I spin on the table before you a top with a somewhat blunt point (Fig. 1). You notice it runs around in a circular or rather a spiral path, and gradually rises to a perpendicular. I strike it quite a hard blow, but do not upset it. I send it flying across the table, or off to the floor, but still it maintains its upright position. You notice that, when it is perpendicular, it stands still; but, if it leans ever so little, it immediately begins to swing or gyrate around a vertical axis. I now change the top for one whose point is very fine and well centered and sharp (Fig. 2). You see that it hardly

Fig. 1. — Blunt-pointed Top.

Fig. 2. — Sharp-pointed Top.

travels at all. I now cause the point to fall into a slight pit in the surface of the table: it ceases to travel, but continues for a very considerable time to swing around a vertical axis, and is remarkably stable, whatever the angle at which it leans. Stopping its traveling has, as you see, no effect upon its stability; but now I put my pencil before the axle and stop the gyration or swinging around. Immediately the power of staying up is gone, and the top falls. I may vary the experiment in every possible way: so long as the axis is inclined, the result is the same; the moment the gyration ceases, the top falls.

In the case of the bicycle there is no gyrating around a vertical axis. Whatever else it may do, it does not do that. Yet, as you saw, gyration is absolutely essential to the effect which Mr. Boys thinks accounts for its stability.

We may, I think, dismiss the top from further consideration; but there is another instrument apparently much closer in its relation to the bicycle. I mean the gyroscope, or rather that form of it which Sir William Thomson calls a gyrostat. Its wheel is upright like the bicycle's (see Figs. 3 and 4). The lower part of

Figs. 3 and 4. — The Gyrostat.

the ring which supports the wheel rests in a kind of trough, to the bottom of which is attached crosswise a piece of metal (best seen in Fig. 3) curved on the lower edge, and with two projecting wires by which it may be drawn back and forth in the plane of the wheel.

I now set the wheel in rapid motion — much more rapid than any bicycle-wheel can go; I place it on a smooth, hard surface — I have here a pane of glass — and leave it to itself. It begins at once, as you see, to revolve around a vertical axis. If it leans little, it revolves slowly; if it leans much, it revolves faster. It will not fall to the table, though I push it, or strike a hard blow. It resists with remarkable force. I now take it by the projecting wires and attempt to make it move in a straight course, as a bicycle does when it spins along the road. Instantly it falls. The rotation of the wheel on its axis was not in the slightest degree interfered with, but the stability vanishes the moment the rotation around the vertical axis ceases. Invariably it falls. Yet you observe the conditions are far more favorable for the effect of gyrostatic action than in the bicycle, for the mass of the rim of our gyrostat is many times heavier in proportion to its size, and its speed incomparably greater. I try the experiment over and over, the result is always the same. No amount of skillful management will make the instrument stay up for an instant if it has to move in a straight line. I submit that these experiments are proof positive that the sustaining power of the bicycle does not come from any gyroscopic action. WHAT KEEPS THE BICYCLER UPRIGHT?

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Diagram illustrating the Com- position of Forces.

��Others find in its going so fast the reason why the bicycle does not fall referring, of course, in a blind way to that principle em- bodied by Newton in his first law : " A body in motion, if left to itself, will continue to move in a straight line forever." A brief examination will, I think, convince you that this, too, fails to account for the effect which we know is somehow produced.

It is another principle in phys- ics that two forces acting at right angles to each other do not inter- fere. Each produces its own effect as fully as if the other did not act. For example, if a certain force sends a body (D, Fig. 5) north at the rate of ten feet in a second, and another force sends it east at the same rate, at the end of one second it will have gone ten feet north and ten feet east, exactly as if each force D had acted alone. Going toward A B does not in the least hinder its go- ing toward B C Now, in case of a bicyclist, his forward motion, whether fast or slow, is at right angles to gravity, hence does not in any way resist it ; and, therefore, as it is gravity that causes him to tilt over, the forward motion will not prevent his falling.

But it may be said that the force of gravity when the 'cycle leans, say to the right, is in fact resolved into two components, one vertical and the other lateral, and it is the latter only that causes the bicyclist to fall. This does not help the matter, for both components are perpendicular to the course of the bicycle, and hence its forward motion can in no way counteract either of them. Unless some other force comes into play, the bicyclist must fall toward whichever side he happens to begin to lean.

Many think they find this counteracting influence in " centrif- ugal force." You all are familiar with the effects of this " force." You feel them every time you turn a corner quickly, whether on foot or in a wagon, or on horseback. The bare-back riders in the circus lean well toward the center of the ring, to escape being thrown outward. We see its effect when the bicyclist spins around a corner. In such cases " centrifugal force " plays an important part, and is the real upholding force.

But centrifugal force is impossible so long as the body moves in the same direction i. e., in a straight line. There must be change of direction, and, other things being equal, this force is greater in proportion to the abruptness of that change ; or, as mathematicians say, the velocity being constant, it varies in- versely as the radius of the curve in which the body moves. The

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larger the radius the smaller the centrifugal force. If the radius of curvature becomes infinite i. e., the curve becomes a straight line the centrifugal force becomes infinitely small, or zero.

So long, therefore, as the bicyclist does not turn corners keeps in a straight course the centrifugal force gives us no assistance whatever in understanding why he keeps his seat so securely. But yet it may be thought that this force, if supplemented by skillful balancing, is sufficient. It keeps the bicycle from falling when turning corners : will not good balancing account for the stability when moving in a straight course ? We are all familiar with the phenomena of balancing one's self. "We know the help a heavy pole gives at such times ; how a person's legs and arms move with startling rapidity in the opposite direction to that in which he feels himself falling. There is nothing of this on the wheel. If the stability was due to balancing, it would not be so very difficult for a bicyclist to sit upon his machine when not in motion., and when its wheels both point in the same direction. I have never seen one that could do it. I suspect, however, that it is not impossible, any more than to stand on the top round of an unsupported ladder. But the ordinary bicyclist can not do it ; and yet, without apparent effort, he rides securely. That his sta- bility is not due to his balancing and to his rapid forward motion combined, is evident when we reflect that if the handles are made immovable, so that neither of the wheels can be turned to the right or left, it is impossible for any ordinary rider, no matter at what speed he may move, to keep from falling for any consider- able time after he once begins to tilt.

Apparently the fact that some can ride " hands off " on a safety wheel contradicts this, for, however it may be on an " ordinary/' on a " safety " the rider can not guide it by the pedals, and as he does not touch the handles of the steering-wheel or the wheel itself, it would seem that his not tilting must be due to good bal- ancing. Experiment, however, proves the contrary. Let the steering-wheel be fixed by tying the handles, or by a clamp on the spindle, so that it can not turn to the right or the left, and then let the 'cyclist try to keep it erect. Balancing won't help, except possibly to delay his fall a few moments. And worse than that, he can't ride hands off at all if he tries to do so only by bal- ancing. The explanation of such riding is not very difficult, but requires some other matters to be treated first. At present all I desire to establish is that in this kind of riding, as well as in all others, the rider's ability to keep from falling to one side for an indefinite time while traveling in a straight line is not due to bal- ancing.

I think you will agree with me that the reasons thus far assigned for the stability of the bicycle cast little or no light

�� � upon the subject. Gyration has nothing to do with it; centrifugal force has no application to it, except when turning corners, or otherwise changing abruptly the direction of the movement; balancing is a detriment rather than an assistance;[2] and rapid motion alone accounts for nothing. Some other explanation is needed; this I shall now attempt to give.

Regarded mathematically as a machine for the application of force, the bicycle is a very simple affair. The weight (Figs. 6 and 7) is applied at the saddle, A, and is so great that the center of

Fig. 6. — An "Ordinary" Bicycle, with Lines of Force.

gravity of the whole is very close to that point. A B and A are the lines of force, B marking the point where the fore wheel rests on the ground, and C where the rear one. In discussing the forces that act on the machine we need consider only these lines, all the other parts being merely for convenience or ornament. It is evident that A can not of itself tilt either backward or forward, since a vertical line from it falls between B and C. In reference to them it is in stable equilibrium, while in regard to side motion its equilibrium is very unstable; the least thing will upset it.

To study the matter more conveniently, I have had a form made which eliminates all unnecessary parts and represents only

Fig. 7.—A "Safety" Bicycle, with Lines of Force.

the lines of force and the weight on the saddle (Fig. 8). It consists, as you see, of two long, slender pieces of pine, and looks like a huge capital A, the cross-piece serving merely to hold the whole more firmly together. At the apex, A, I have placed a few pounds of lead to represent the rider's weight.

Fig. 8.—Apparatus illustrating the Way a Bicycle is kept Upright.

In the older form of the bicycle, the wheel in front is very much the larger. The corresponding leg, A B (Fig. 8), is much steeper and shorter than the other. In "safety cycles" it is just the reverse, the rear leg being steeper and shorter, while the two wheels are of nearly the same size. As the theory of both machines is the same, I shall, the present, for speak only of the former.

For convenience in handling, and that it may be better seen, I place the foot C, the rear one, on the table, and hold the other, B, in my hand, and at the same height from the floor. Now, notice: the weight at the apex, or saddle, begins to tilt to the WHAT KEEPS THE BICYCLER UPRIGHT? 773

right ; I quickly move my hand to the right till it comes under the weight. If the saddle tilts to the left, I move my hand quickly to the left. In every case, by moving my hand more rapidly than the weight tilts, I bring the point of support under it. It is very easy in this way to keep the weight from falling ; and that is the way the bicycle is kept upright.

But you will ask, How can the rider move the point of sup- port when it is on the ground, and several feet out of his reach ? He does it by turning the wheel to the right or left, as may be necessary that is, by pulling the cross-bar to the right or left, and thus turning the forked spindle between whose arms the steering-wheel is held and guided.

But, some one will say, How does turning the wheel bring the point of support to the right or left whichever the machine may happen to be leaning ?

Let us suppose a 'cyclist mounted on his wheel and riding, say, toward the north. He finds himself beginning to tilt toward his right. He is now going not only north with the machine, but east also. He turns the wheel eastward. The point of support, B (Fig. 6), must of necessity travel in the plane of the wheel ; hence it at once begins to go eastward, and, as it moves much faster than the rider tilts, it quickly gets under him, and the machine is again upright. To one standing at a distance, in front or rear, the bot- tom of the wheel will be seen to move to the right and left, just as I moved the foot of the skeleton frame a moment ago.

I conclude, then, that the stability of the bicycle is due to> turning the wheel to the right or left, whichever way the leaning is, and thus keeping the point of support under the rider, just as a boy keeps upright on his finger a broomstick standing on its smallest end.

It may be questioned whether the bottom point of the wheel really travels faster than the weight at the saddle tilts over, and, if it does not, then the explanation which I have been giv- ing fails.

By an easy calculation, based on the well-known principle' that the velocity of a body moving under the influence of gravitation varies as the square root of the height from which it has fallen, irrespective of the character of the path it has described, I find that when the rider's seat is, e. g., sixty inches high, and the ma- chine has inclined, say, six inches out of the perpendicular, it is at that instant, if free to fall, tilting over at the rate of much less than a mile an hour. But six inches is a large amount to lean a good 'cyclist does not lean that much we will suppose him out of plumb only three inches ; then his lateral movement will be at the rate of only some twenty-two hundred feet in an hour.. If the tilt is less, the falling rate will be less. To keep the center of

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gravity over the base, the bottom of the wheel needs only to move to the right or left whichever the machine is leaning some- what faster than these slow rates. There is no great difficulty in doing this, for, if the bicycle is going eight miles an hour, it is necessary to change its course only about seven degrees ; if four miles, then only about fourteen degrees ; if two miles, then about twenty-eight degrees. The greater the speed, the less the angle : at sixteen miles an hour, the wheel would need to be turned less than two degrees. From which follows the fact, well known to 'cyclists, that the slower the machine is traveling the more the handles must be turned, and the more difficult to keep from falling.

From the fact that the bicycle is kept erect by keeping its point of support under it, like a pole standing upright on one's finger, some curious and, to most persons, quite surprising results follow. I have here three rods, respectively one foot, three feet, and seven feet long. I hold the last, as you see, very easily ; the second not so easily; and the first only with considerable diffi- culty. I now put a cap of lead weighing four or five pounds on the top of each, and then again support them as before. In every case it is now easier to keep them from falling. Hence, in a bicycle, the higher and the heavier the load, the less the danger of falling ; and, as most of the weight is in the saddle, the center of gravity of the whole is very near it, and it is the height of that, and not the size of the wheel, that affects the lateral stabil- ity. A rider with a load on his back, whether a bag of grain or a man sitting on his shoulders, is by all that the more safe from falling either to the right or left, however it may be as to headers.

Experts sometimes ride for a considerable distance with both legs over the cross-bar. But there is nothing strange in this, for placing their legs in that position only raises the center of grav- ity, and hence really adds to the stability. If in some way they can manage to turn the cross-bar, they can ride without difficulty until the momentum is exhausted.

A much more difficult feat is to ride on one wheel. The small wheel the rider holding the other in the air is most easily man- aged. It is merely a case of supporting on a small base a long, upright body. One keeps moving the point of support so as to 'bring it under the center of gravity. It needs only a quick eye and a steady hand. It is much more difficult when the 'cyclist uses only the big wheel, the other having been removed, for he is liable to fall forward or backward, as well as to either side. To avoid the first and second, he leans forward a little beyond his base, and would pitch headlong, but that he drives the wheel for- ward by means of the treadles just fast enough to prevent it. "We all do the same thing when we walk. We lean so far forward

�� � that we would fall, did we not keep moving our feet fast enough to prevent it. On the single wheel most of us would fail, because from lack of experience we would make the wheel go too fast, and so would fall backward; or else, not fast enough to keep from falling on our faces. As to falling sidewise, that is prevented exactly as when both wheels are used — the rider turns the cross-bar to the right or left, and propels the machine in that direction. Experience, a level head, and a steady hand tell how far to turn it.

From mere inspection of Fig. 6 we see that safety against headers varies inversely as the height of the saddle, and directly as the distance from the foot of the perpendicular A D to the forward point of support B (Figs. 6 and 7). In other words, the higher the saddle, the greater the danger of headers; and the farther back, the less the danger.

As to the law of lateral safety — i. e., against falling sidewise — it is in one respect the reverse of the other, for the greater the height of the saddle, the easier not to fall to either side, just as it is easier to keep upright on the end of my finger a long stick than a short one.

↑At the close of the reading of the paper, a teacher of the art of riding the bicycle, a man of large experience, arose, and, in the course of his remarks, said that one of the chief difficulties he had to contend with in teaching beginners to ride, was to induce them to give up all idea of balancing; that till this was done they could not ride well a striking corroboration of the theoretical conclusion arrived at by the writer of this paper.